CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Seminar Abstracts

Morton Gurtin, Carnegie Mellon University

Title: The formulation of gradient theories for single-crystal plasticity at small length scales: size effects

TUESDAY, February 17, 2008
Time: 1:30 P.M.
Location: PPB 300

Abstract: This talk discusses a finite-deformation, gradient theory of single crystal plasticity --- concentrating on the steps involved in its formulation. The theory is based on a system of microscopic force balances, one balance for each slip system, derived from the principle of virtual power, and a mechanical version of the second law that includes, via the microscopic forces, work performed during plastic flow. When combined with thermodynamically consistent constitutive relations the microscopic force balances become flow rules for the individual slip systems. Because these flow rules are in the form of partial differential equations requiring boundary conditions, they are nonlocal. The chief new ingredient in the theory is a free energy dependent on densities of geometrically necessary dislocations. Predictions of the theory obtained via computations are shown to agree well with discrete dislocation simulations. Further --- using published experimental data for several polycrystalline materials --- it is shown that the theory explains the $D^{-1}$ dependence of the initial yield stress on the grain size $D$ in the submicron to several micron range.